Here, make is used in a context of "to cause something":
You make me cry — meaning, I was not crying, but because of you I start.
Become is simply "to change {one's own} state".
Imagine Alice sees a sad Bob. Alice tells a funny joke to Bob, and he becomes happy. The following sentences are all valid:
- Alice made Bob happy;
- Bob became happy;
- Alice made Bob
to (1) become happy;
So, as you see, to make applies to a causing subject, while to become applies to an object that changes.
(1) Thanks to @StoneyB; make takes bare infinitive, so can't use to here.
"If he became president, what would that mean to ..."
The ideas could be expressed in a number of ways. It is acceptable as is.
The first phrase is a conditional clause and the second represents the results, if the condition is met, in the form of an inquiry. The condition can be in the past, as the results cannot occur until the condition is met.
If he becomes president....
If the condition is in the present, then the inquiry in this case should be:
what will that mean...?
If the condition is met in the present, then the results need to be beyond the present (the future).
In older common usage the wording might have been:
Should he become president, what would that mean...?
But such usage is rare today.
But I'd never use the conjugate the verb in the past when it's an something that might still come to pass.
It would be the order of events that determine tense, as a general rule, if a
conditional is used,and, a situation counter to fact is created. "If he became president" suggests he "could have" become president, but clearly means he is not president. It also means that if he were president, he became president before the present. That is OK, as the results of his being president
cannot be until he is president. But, whether he "became" or
becomes" this has not occurred, so the results are in a future time. Whether one starts in the past and goes forward, or begins now and goes forward, the relative time is correct. The use of a conditional suspends fact and time becomes relative, not factual.
Best Answer
I don't find either got happy or became happy to be particularly natural. I would simply use was happy, and leave whether that is an observation or a contrast with a previous state to be understood from context:
Leaving that aside, it is true that some meanings of the extremely versatile get mean become, specifically:
[ODO] Worth noting is the usage note:
In other words, get happy would be more common in conversation and in informal writing, whereas become happy would be more acceptable in formal registers. That is broad a generalization, but it has usage implications.
Get has a somewhat greater connotation of agency or intent, perhaps because many of its other meanings are causative, and refer to inducement, deliberate movement, or inflicting injury or punishment. If I say I got drunk on cough syrup, I may be interpreted as intentionally drinking cough syrup to get drunk. If I say I became drunk on cough syrup, I am distancing myself from the act, saying the drunkenness was unintentional.
Become being more distant and thus "softer," it is much rarer as an imperative, in verbal communication or informal writing. Get is more direct, whether you want to be forceful— Get ready! Get cracking! Get out!— or more personal— Get well soon!
For additional usage notes, BBC Learning English has a unit on 'Get' and 'become'. At EL&U see Is “get” (in the sense of “become/make”) appropriate for formal writing? and He was getting vs being beaten among others.
Note also that get is involved in a large number of idioms, some vulgar. If John and Mary are lollygagging around the office, their manager must be careful about saying The two of you should get busy as that can be taken to mean that they should have sexual relations. Similarly, get happy to Americans is more likely to be taken to mean getting drunk or high on marijuana than as a reference to a Judy Garland song (which was probably performed by a Judy Garland who was both).